Who: Esben Mølgaard (CP3-Origins)
When: Sunday, June 15, 2014
In this thesis, we will present the results of our studies into the nature of four–dimensional, non-supersymmetric quantum field theory, particularly that of renormalization group flows. This is of course a vast subject and we could not hope to cover it all. We begin our presentation by discussing two rather different models that we will return to several times during the course of the thesis. The first is the standard model of particle physics, where we put a great emphasis on the Higgs field and its particle, the second is an SU(Nc) toy model which has been found to have many interesting properties.
We then proceed to introduce the concept of renormalization, and dedicate an extended section to a new method that we have developed for the calculation of (especially) beta functions. We also take time to discuss fixed points in gauge theories, and how the presence or absence of these is determined by the parameters of the theory in question.
Next, we study the conjectured a theorem, i.e., the proposal that there exists a function a of the couplings in a four-dimensional quantum field theory which is monotonic along any renormalization group flow. We test the weak form of this conjecture, which states that a is larger at UV fixed points than at IR fixed points, and find that this holds in the toy model even when none of the fixed points is Gaussian.
From our investigations into the a theorem, we discovered that to preserve the symmetries of a gauge-Yukawa theory, it is necessary to run the gauge couplings with a beta function that is calculated to one higher loop order than the Yukawa beta functions, which must in turn be computed to one higher loop order than the quartic beta functions. We use this very important result to refine computations done previously by others regarding the stability of the standard model vacuum.
Finally, we consider the renormalization group flows of a model inspired by the standard model lepton sector when the beta functions are computed to different loop orders. We use this to give quantitative statements regarding the trustworthiness of perturbation theory.